Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling

We present a new method for Bayesian Markov Chain Monte Carlo-based inference in certain types of stochastic models, suitable for modeling noisy epidemic data. We apply the so-called uniformization representation of a Markov process, in order to efficiently generate appropriate conditional distributions in the Gibbs sampler algorithm. The approach is shown to work well in various data-poor settings, that is, when only partial information about the epidemic process is available, as illustrated on the synthetic data from SIR-type epidemics and the Center for Disease Control and Prevention data from the onset of the H1N1 pandemic in the United States.